Sr Examen
Ecuación diferencial cos(x+y)dx=xsin(x+y)dx+xsin(x+y)dy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d
cos(x + y(x)) = x*sin(x + y(x)) + x*--(y(x))*sin(x + y(x))
dx
$$\cos{\left(x + y{\left(x \right)} \right)} = x \sin{\left(x + y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} + x \sin{\left(x + y{\left(x \right)} \right)}$$
cos(x + y) = x*sin(x + y)*y' + x*sin(x + y)
Respuesta
[src]
/C1\
y(x) = -x + acos|--|
\x /
$$y{\left(x \right)} = - x + \operatorname{acos}{\left(\frac{C_{1}}{x} \right)}$$
/C1\
y(x) = -x - acos|--| + 2*pi
\x /
$$y{\left(x \right)} = - x - \operatorname{acos}{\left(\frac{C_{1}}{x} \right)} + 2 \pi$$
Clasificación
factorable
1st exact
lie group
1st exact Integral